Question

Take away: 

\[\frac{2}{3}ac - \frac{5}{7}ab + \frac{2}{3}bc\text { from } \frac{3}{2}ab - \frac{7}{4}ac - \frac{5}{6}bc\]

Answer 1

The difference is given by:

\[\left( \frac{3}{2}ab - \frac{7}{4}ac - \frac{5}{6}bc \right) - \left( \frac{2}{3}ac - \frac{5}{7}ab + \frac{2}{3}bc \right)\]

\[ = \frac{3}{2}ab-\frac{7}{4}ac-\frac{5}{6}bc-\frac{2}{3}ac+\frac{5}{7}ab-\frac{2}{3}bc\]

\[= \frac{3}{2}ab + \frac{5}{7}ab - \frac{7}{4}ac - \frac{2}{3}ac - \frac{5}{6}bc - \frac{2}{3}bc\] (Collecting like terms )

= \[\left( \frac{21 + 10}{14} \right)ab + \left( \frac{- 21 - 8}{12} \right)ac + \left( \frac{- 5 - 4}{6} \right)bc\]

\[=\frac{31}{14}ab-\frac{29}{12}ac-\frac{3}{2}bc\]           (Combining like terms )